Stationary configurations of two extreme black holes obtainable from the Kinnersley-Chitre solution

Abstract

Stationary axisymmetric systems of two extreme Kerr sources separated by a massless strut, which arise as subfamilies of the well-known Kinnersley-Chitre solution, are studied. We present explicit analytical formulas for the individual masses and angular momenta of the constituents and establish the range of the parameters for which such systems can be regarded as describing black holes. The mass-angular momentum relations and the interaction force in the black-hole configurations are also analyzed. Furthermore, we construct a charging generalization of the Kinnersley-Chitre metric and, as applications of the general formulas obtained, discuss two special cases describing a pair of identical co-and counterrotating extreme Kerr-Newman black holes kept apart by a conical singularity. From our analysis it follows in particular that the equality m 2 − a 2 − e 2 = 0 relating the mass, angular momentum per unit mass and electric charge of a single Kerr-Newman extreme black hole is no longer verified by the analogous extreme black-hole constituents in binary configurations.The well-known Kinnersley-Chitre (KC) solution [1] represents the extremal limit of the double-Kerr spacetime [2], and as such permits one to describe stationary axisymmetric configurations of two extreme Kerr sources. In the case of the balancing constituents [3][4][5] it can be shown that at least one of these constituents is endowed with a negative mass, which spoils the interpretation of those binary configurations as describing two black holes. This naturally motivates the search for (and subsequent analysis of) the systems composed of two extreme black holes separated by a massless strut (conical singularity [6]) which may arise for instance in the context of some more general nonstationary axisymmetric scenarios as momentary stationary data [7] for interacting black holes. In the recent paper [8], various binary configurations of extreme Kerr sources with a middle strut were obtained in the analytical form thanks to a new simple representation of the KC metric, and some examples were given in which both extreme constituents can be envisaged as black holes due to the positiveness of their Komar [9] masses and regularity of the corresponding spacetimes outside the horizons.The present paper pursues the following two main goals. First, we would like to amplify the initial analysis of the novel binary configurations discovered in [8], with the general analytic formulas for the individual Komar quantities (masses and angular momenta) characterizing the extreme constituents in the case of all four subfamilies of the KC solution from [8] whose total mass can take positive values. This will allow us to make a systematic study of the mass-angular momentum relations in the corresponding purely black-hole binary systems. Second, by using the Harrison-Ernst invariance transformation [10,11], we shall construct a charging generalization of KC metric, which will permit us to get the first known configurations of two extreme Kerr-Newman (KN) constituents [12]...

Generalized near horizon extreme binary black hole geometry

“…This paper generalizes the construction studied recently in [11] for the equal mass case. Figure 2: The diagram represents a spatial cross section of the two extremal co-rotating BHs metric [22] reproduced in Appendix A. The geometry (in black and gray) has an asymptotically Minkowskian region and a single black hole throat of mass M 1 + M 2 which divides into two throats of masses M 1 and M 2 .…”

“…3 Pierced-NHEK: near horizon limit at finite separation In this section it is shown that there exists a well-defined near-horizon limit of the stationary binary extreme Kerr solution [22,21] even when the BHs, which are held apart by a conical singularity, are separated by a finite distance. The near-horizon region is composed of two disconnected NHEK-like geometries, one near each of the BHs.…”

“…We proceed to compute the near horizon geometry of extremal nonidentical binary Kerr black holes solution, that we are going to refer to as "Generalized-NHEK2". The solution of extremal BBHs [22] -that we reproduced in Appendix A -has a rather more compact representation in Weyl coordinates. We therefore perform the scaling computations in these coordinates.…”

“…Let us now consider the physical parameters of the Generalized-NHEK2 solution. As we did at the level of the geometry, the near-horizon limiting procedure can be applied to the original physical parameters found in [22] (also reviewed here in App. A).…”

The Bretón–Manko equatorially antisymmetric binary configuration revisited

“…The Ernst potentials and metric functions of the extreme BM solution have been worked out in explicit form in the paper [33].…”